What happens / why do motors stall?

[Matt Leese]

I think that you're problems come from a misunderstanding voltage. Voltage doesn't flow. It's best to think of voltage as a potential. Current flows from higher potential to lower potential. Voltages can be though of as either positive or negative. It all depends on which lead you treat as the positive side (this is the polarity; if you switch which lead you consider positive, it's equivalent to multiplying the voltage by -1).

The other important thing to remember is Kirchoff's Voltage Law which says that in a complete loop, the sum of the voltages will be zero. In this case, you add the battery power supply of 12 V, the voltage drop due to the internal resistance of the motor, and the voltage drop due to the back EMF. Or:
Vs - Vr - Vemf = 0

Now, Vs is constant at 12 V. Vemf is dependent on the speed of the motor. Vr is dependent on the current, I, and the resistance, R. R is constant. And Vr = I * R.
Through this, you can see that as the back EMF increases, Vr will decrease and therefore I will decrease. As EMF decreases, Vr will increase and therefore I will increase. Because the back EMF is directly proportional to the speed of the motor, the current is inversely proportional to the speed of the motor. Hence, at stall, the current through the motor is very high.

This relates to power through P= V * I. It's important to take the power across the entire system and not just the back EMF or the resistance. In this case, V is constant at 12 V. Therefore, power is dependent on the current. This means that as the speed of the motor decreases, power increases. Or, the power is inversely proportional to the speed of the motor.

Matt